# How do you simplify sqrt(75) ?

Sep 11, 2016

$\sqrt{75} = 5 \sqrt{3}$

#### Explanation:

First factorise $75$:

$75 = 3 \cdot 5 \cdot 5$

Next note that if $a , b \ge 0$ then:

$\sqrt{a b} = \sqrt{a} \sqrt{b}$

Also if $a \ge 0$ then:

$\sqrt{{a}^{2}} = a$

So we find:

$\sqrt{75} = \sqrt{{5}^{2} \cdot 3} = \sqrt{{5}^{2}} \cdot \sqrt{3} = 5 \sqrt{3}$